1. Field of the Invention
The invention generally relates to electronics. In particular, the invention relates to amplifier applications, such as amplifiers in RF transmitters.
2. Description of the Related Art
Amplifiers are used in a variety of electronic devices. For example, radio frequency (RF) power amplifiers prepare a signal for transmission by increasing the power of the signal. The signal, such as a television signal, radio signal, or cell phone signal, can be transmitted through the air via an antenna. Other signals, such as those found in cable-TV systems, are transmitted through wires.
Two of the main parameters describing an amplifier are its gain and its linearity (absence of distortion). In an amplifier implemented using MOS transistors, these two parameters are related to the other by the transconductance of the MOS transistor.
Three main sources of nonlinear distortion exist for MOS transistors: (1) Transconductance (gm); (2) Gate capacitances (cgs, cgd); and (3) Junction capacitances (cjs, cjd).
Transconductance
Distortion due to (1) transconductance will be discussed in further detail in the following. For a MOS transistor, transconductance gm is expressed in Equation 1.
                              g          m                =                              ∂                          I              d                                            ∂                          V              gs                                                          Eqn        ⁢                                  ⁢        1            
In Equation 1, Id is the drain current and Vgs is the gate-source voltage. The transconductance gm is not a linear function of Vgs, as shown in the power series expansion of drain current expressed in Equation 2:
                                          I            d                    =                                                    a                1                            ⁢                              V                gs                                      +                                          a                2                            ⁢                              V                gs                2                                      +                                          a                3                            ⁢                              V                gs                3                                      +            …                          ⁢                                  ⁢                                            where              ⁢                                                          ⁢                              a                1                                      =                          g              m                                ,                                          ⁢                                    a              2                        =                                          ∂                                  g                  m                                                            ∂                                  V                  gs                                                              ,                                          ⁢                                    a              3                        =                                                            ∂                  2                                ⁢                                  g                  m                                                            ∂                                  V                  gs                  2                                                              ,                                          ⁢                      etc            ⁢            …                                              Eqn        ⁢                                  ⁢        2            
Terms a2 and a3 represent the second-order and third-order transconductance distortion coefficients of the MOS transistor. Second-order distortion is proportional to the first derivative of transconductance with respect to Vgs. Likewise, third-order distortion is proportional to the second derivative of transconductance with respect to Vgs.
The linear coefficient a1=gm, typically demonstrates the trend (plotted for an arbitrarily selected sample MOS device) in FIG. 1. Second-order distortion, represented by coefficient a2, is shown in FIG. 2. Third-order distortion, represented by coefficient a3, is shown in the FIG. 3.
Biasing the transistor with gate-source voltage Vgs indicated by point “A” in FIG. 3 can yield an amplifier with reduced third order distortion. Many circuits approach the issue of even-order distortion, e.g., second order, by utilizing differential topologies. Thus, the designer is left to deal with only odd order distortion, out of which, third order typically dominates.
The small-signal gain of a MOS transistor amplifier shown in FIG. 4 is expressed in Equation 3.
                              A          v                =                                            V              o                                      V              i                                ≈                                    -                              g                m                                      ⁢            Z                                              Eqn        ⁢                                  ⁢        3            
In Equation 3, gm represents the transistor transconductance, and Z represents the load impedance in ohms present at the drain of the MOS transistor. Resistor R1 and voltage VB are used to set the DC current flowing in the device, setting the transistor transconductance gm.
The gain of an amplifier can be adjusted by changing the load impedance and/or the transconductance of the transistor. Typically, the load impedance of an amplifier is dictated by matching requirements of the system and cannot be easily changed. One parameter that can be varied is the transconductance of the transistor. However, changing the transconductance to adjust an amplifier's gain can affect the amplifier's linearity by moving the zero-crossing point A in FIG. 3, in this case, operating in a sub-optimal region.